6 Letter dividend - 3rd Grade...

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dividend The number that is to be divided in a division problem

dividend, divisor, quotient The parts of a division problem. There are two ways to record division.

10 ÷ 2 = 5

dividend divisor quotient

2 q w 10

Dear Family,

During the next few weeks, our math class will be learning about division. We will learn how division is related to subtraction, and how multiplication and division are inverse operations.

You can expect to see homework that provides practice with division.

Here is a sample of how your child will be taught to use repeated subtraction to solve division problems.

6

Chapter 6 P93

5divisor

dividend

quotient

This is how we will be using repeated subtraction to divide.

STEP 1

Start with the dividend and subtract the divisor until you reach 0.

15 ÷ 5 = ____

15− 5 10

10− 5 5

5−5 0

Counting Back on a Number Line

Counting back on a

number line is another

way to find a quotient.

On a 0–15 number line,

for example, start at 15

and count back by 5s to 0.

Then count the number of

jumps on a number line

(3 jumps) to find that

15 ÷ 5 = 3.

STEP 2

Count the number of times you subtract 5.

15− 5 10

10− 5 5

5− 5 0

There are 3 groups of 5 in 15.

STEP 3

Record the quotient.

15 ÷ 5 = 3, or

5 q w 15

Fifteen divided by 5 equals 3.

(3 times)3

Use Repeated Subtraction to Divide

ActivityDisplay a number of objects that are divisible by 5. Have your child use repeated

subtraction to solve division problems. For example: “Here are 20 crayons. I want

to subtract 5 crayons at a time until there are no crayons left. How many times can

I subtract?” Check answers by arranging the objects.

para la casaCartaCarta

Capítulo

Pistas

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dividendo El número que se divide en

un problema de división.

dividendo, divisor, cociente Las

partes de un problema de división. Hay

dos maneras de anotar la división.

10 ÷ 2 = 5

dividendo divisor cociente

2 q w 10

Estimada familia,

Durante las próximas semanas, nuestra clase de matemáticas aprenderá sobre la división. Aprenderemos sobre cómo la división se relaciona con la resta, y cómo la multiplicación y la división son operaciones inversas.

Pueden esperar ver tareas que sirven para practicar la división.

Esta es una muestra de cómo su hijo o hija aprenderá a usar la resta repetida para resolver problemas de división.

6

5divisor

dividendo

cociente

Así es como usaremos la resta repetida para dividir. Contar hacia atrás en una recta numérica

Contar hacia atrás en

una recta numérica es

otra manera de hallar un

cociente. En una recta

numérica de 0–15, por

ejemplo, comience en 15

y cuente hacia atrás de

5 en 5 hasta 0. Después

cuente la cantidad de

saltos que da en la recta

numérica (3 saltos), para

hallar que 15 ÷ 5 = 3.

PASO 1

Comience con el dividendo y réstele el divisor hasta llegar a 0.

15 ÷ 5 = ____

15−5 10

10−5 5

5−5 0

PASO 2

Cuente la cantidad de veces que restó 5. 15−5 10

10−5 5

5−5 0

Hay 3 grupos de 5 en 15.

PASO 3

Anote el cociente.

15 ÷ 5 = 3, o

5 q w 15

Quince dividido entre 5 es igual a 3.

Usar la resta repetida para dividir

ActividadMuestre una cantidad de objetos que sea divisible entre 5. Pida a su hijo o hija que use la

resta repetida para resolver problemas de división. Por ejemplo: “Aquí hay 20 crayolas.

Quiero restar 5 crayolas a la vez hasta que no queden crayolas. ¿Cuántas veces puedo

restar?”. Compruebe las respuestas ordenando los objetos.

(3 veces)3

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PROBLEM SOLVINGLesson 6.1

Solve each problem.

Problem Solving • Model Division

1. Six customers at a toy store bought 18 jump

ropes. Each customer bought the same

number of jump ropes. How many jump ropes

did each customer buy?

_____

2. Hiro has 36 pictures of his summer trip. He

wants to put them in an album. Each page of

the album holds 4 pictures. How many pages

will Hiro need for his pictures?

_____

3. Katia has 42 crayons in a box. She buys a

storage bin that has 6 sections. She puts the

same number of crayons in each section. How

many crayons does Katia put in each section of

the storage bin?

_____

4. Ms. Taylor’s students give cards to each of

the 3 class parent helpers. There are

24 cards. How many cards will each helper

get if the students give an equal number of

cards to each helper?

_____

5. Jamie divides 20 baseball stickers equally

among 5 of his friends. How many stickers

does each friend get?

_____

Chapter 6 P95

3 jump ropes

COMMON CORE STANDARD—3.OA.3. Represent and solve problems involving multiplication and division.

7 7 777

77

77

7

1 32 4 65Piano Practice Hours

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5. Count equal groups to find how many

there are.

6. What is another way to group the

factors?

(3 × 2) × 5

3. Find the unknown factor.

7 3 ■ 5 56

4. How many students practiced the

piano more than 3 hours a week?

Spiral Review (3.OA.1, 3.OA.4, 3.OA.5, 3.MD.4)

Lesson Check (3.OA.3)

1. Maria buys 15 apples at the store and

places them into bags. She puts 5

apples into each bag. How many bags

does Maria use for all the apples?

2. Tom’s neighbor is fixing a section of

his walkway. He has 32 bricks that he

is placing in 8 equal rows. How many

bricks will Tom’s neighbor place in

each row?

Problem SolvingProblem Solving

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Lesson 6.2

Size of Equal Groups

Chapter 6 P97

Use counters or draw a quick picture. Make equal

groups. Complete the table.

Counters Number of Equal Groups Number in Each Group

1. 15 3 52. 21 7

3. 28 7

4. 32 4

5. 9 3

6. 18 3

7. 20 5

8. 16 8

9. 35 5

10. 24 3

11. Alicia has 12 eggs that she will use

to make 4 different cookie recipes. If

each recipe calls for the same number

of eggs, how many eggs will she use in

each recipe?

12. Brett picked 27 flowers from the

garden. He plans to give an equal

number of flowers to each of 3

people. How many flowers will each

person get?


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5. What is the unknown factor?

7 3 ■ 5 35

6. Describe the pattern in the table.

3. Each table has 4 legs. How many legs

do 4 tables have?

4. Tina has 3 stacks of 5 CDs on each

of 3 shelves. How many CDs does

she have?

Spiral Review (3.OA.1, 3.OA.4, 3.OA.5, 3.OA.9)


1. Ryan has 21 pencils. He wants to

put the same number of pencils

in each of 3 pencil holders. How

many pencils will he put in each

pencil holder?

2. Corrine is setting out 24 plates on

6 tables for a dinner. She sets the

same number of plates on each table.

How many plates does Corrine set on

each table?

Number of packs 1 2 3 4 5

Number of yo-yos 3 6 9 12 ?


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Lesson 6.3

Number of Equal Groups

Chapter 6 P99

Draw counters on your MathBoard. Then circle

equal groups. Complete the table.

Counters Number of Equal Groups Number in Each Group

1. 24 3 8

2. 35 7

3. 30 5

4. 16 4

5. 12 6

6. 36 9

7. 18 3

8. 15 5

9. 28 4

10. 27 3

11. In his bookstore, Toby places

21 books on shelves, with 7 books

on each shelf. How many shelves

does Toby need?

12. Mr. Holden has 32 quarters in stacks

of 4 on his desk. How many stacks of

quarters are on his desk?


PREPTEST

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5. What property does the number

sentence show?

8 1 0 5 8

6. Each month for 6 months, Kelsey

completes 5 paintings. How many

more paintings does she need to

complete before she has completed

38 paintings?

3. What multiplication sentence does

the array show?

4. Austin buys 4 boxes of nails for his

project. There are 30 nails in each

box. How many nails does Austin

buy in all?

Spiral Review (3.OA.3, 3.OA.8, 3.OA.9, 3.NBT.3)

1. Ramon works at a clothing store. He

puts 24 pairs of jeans into stacks of 8.

How many stacks does Ramon make?

2. There are 36 people waiting in line

for a hay ride. Only 6 people can ride

on each wagon. If each wagon is full,

how many wagons are needed for all

36 people?



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Lesson 6.4

Chapter 6 P101

Model with Bar Models

Write a division equation for the picture.

Complete the bar model to solve. Then write a

division equation for the bar model.

1.

3.

2.

4.

7. Jalyn collected 24 stones. She put

them in 4 equal piles. How many

stones are in each pile?

5. There are 15 postcards in 3 equal

stacks. How many postcards are in

each stack?

15 postcards

_______

6. There are 21 key rings. How many

groups of 3 key rings can you make?

21 key rings

3 3

groups

_______

8. Tanner has 30 stickers. He puts

6 stickers on each page. On how

many pages does he put stickers?


27 ÷ 3 = 9 or 27 ÷ 9 = 3

2 3 410

Number ofComputers at Home

7 7 7 77 77 7

7

77777

77777

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Spiral Review (3.OA.5, 3.OA.7, 3.MD.4)


3. Angie puts 1 stamp on each

envelope. She puts stamps on

7 envelopes. How many stamps

does Angie use?

Use the line plot for 5–6.

5. How many families have

1 computer at home?

6. How many families have more than

1 computer at home?

4. A carnival ride has 8 cars. Each car

holds 4 people. How many people

are on the ride if all the cars are full?

1. Jack and his little sister are stacking

24 blocks. They put the blocks in

3 equal stacks. How many blocks

are in each stack?

2. Melissa made 45 greeting cards.

She put them in 5 equal piles.

How many cards did she put in

each pile?


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Lesson 6.5

Chapter 6 P103

Relate Subtraction and Division

Write a division equation.

Use repeated subtraction or a number line to solve.

1. 16

− 4

_

12

12

− 4

_

8

8

− 4

_

4

4

− 4

_

0

3.

2 3 4 5 6 7 8 9 1010

2.

2 3 4 5 6 7 8 9 10 11 1210

4. 20

− 5

_

15

15

− 5

_

10

10

− 5

_

5

5

− 5

_

0

9. Mrs. Costa has 18 pencils. She

gives 9 pencils to each of her

children for school. How many

children does Mrs. Costa have?

10. Boël decides to plant rose bushes in

her garden. She has 24 bushes. She

places 6 bushes in each row. How

many rows of rose bushes does she

plant in her garden?

5. 28 ÷ 7 = _ 6. 18 ÷ 6 = _

7. 8q ww 40 8. 9q ww 36

16 ÷ 4 = 4


12108642

0Jill Ben Madi Eli

Num

ber

of H

ours

Student

Hours Volunteered

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Use the graph for 5–6. 5. How many hours did Eli volunteer?

6. Madi volunteered 2 hours less than

Jill. At what number should the bar

for Madi end?

3. Ellen buys 4 bags of oranges. There

are 6 oranges in each bag. How

many oranges does Ellen buy?

4. Each month for 7 months, Samuel

mows 3 lawns. How many more

lawns does he need to mow before

he has mowed 29 lawns?

1. What division equation is shown?

2 3 4 5 6 7 8 9 10 11 1210

2. Isabella has 35 cups of dog food.

She feeds her dogs 5 cups of food

each day. For how many days will

the dog food last?


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Lesson 6.6

Chapter 6 P105

Model with Arrays

1. How many rows of 4 are in 12?

____


____


____


____

5. 20 tiles in 5 rows

____


____

Make an array. Then write a division equation.

Use square tiles to make an array. Solve.

3 rows

9. A dressmaker has 24 buttons. He

needs 3 buttons to make one dress.

How many dresses can he make with

24 buttons?

_______

10. Liana buys 36 party favors for her

9 guests. She gives an equal number of

favors to each guest. How many party

favors does each guest get?

_______


____


____

COMMON CORE STANDARD—3.OA.3 Represent and solve problems involving multiplication and division.

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Spiral Review (3.OA.1, 3.OA.4, 3.OA.5, 3.OA.7)


1. Mr. Canton places 24 desks in

6 equal rows. How many desks

are in each row?

2. Which division equation is shown by

the array?

3. Amy has 2 rows of 4 sports trophies

on each of her 3 shelves. How many

sports trophies does Amy have?

5. Sam has 7 stacks with 4 quarters

each. How many quarters does

Sam have?

4. What is the unknown factor?

9 × p = 45

6. How can you skip count to find how

many counters in all?

Lesson 6.7ALGEBRA


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Relate Multiplication and Division

4. 4 × _ = 28 28 ÷ 4 = _ 5. 6 × _ = 36 36 ÷ 6 = _

Complete the equations.

Complete the equations.

8. 9 × _ = 27 27 ÷ 9 = _ 9. 2 × _ = 16 16 ÷ 2 = _

1.

5 rows of _ = 20

5 × _ = 20

20 ÷ 5 = _

2.

4 rows of _ = 24

4 × _ = 24

24 ÷ 4 = _

3.

3 rows of _ = 24

3 × _ = 24

24 ÷ 3 = _

12. Mr. Martin buys 36 muffins for a class

breakfast. He places them on plates

for his students. If he places 9 muffins

on each plate, how many plates does

Mr. Martin use?

_______

13. Ralph read 18 books during his

summer vacation. He read the same

number of books each month for

3 months. How many books did he

read each month?

_______

Chapter 6 P107

6. 7 × _ = 35 35 ÷ 7 = _ 7. 7 × _ = 21 21 ÷ 7 = _

10. 4 × _ = 36 36 ÷ 4 = _ 11. 8 × _ = 40 40 ÷ 8 = _

COMMON CORE STANDARD—3.OA.6. Understand properties of multiplication and the relationship between multiplication and division.

44

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3. Sam and Jesse can wash 5 cars each

hour. They work for 7 hours each day

over 2 days. How many cars did Sam

and Jesse wash?

5. The key for a picture graph showing

the number of books students read

is: Each = 2 books. How many

books did Nancy read if she has

by her name?

4. Keisha skip counted to find how

many counters in all. How many

equal groups are there?

_ groups of 5

6. Jan surveyed her friends to find

their favorite season. She recorded |||| ||| for summer. How many

people chose summer as their

favorite season?

1. What number will complete

the equations?

6 × = 24

24 ÷ 6 =

2. Alice has 14 seashells. She divides

them equally between her 2 sisters.

How many seashells does each

sister get?



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Chapter 6 P109

Write Related Facts

Write the related facts for the array.

1.

____

____

____

____

4. 3, 7, 21

____

____

____

____

2.

____

____

____

____

5. 2, 9, 18

____

____

____

____

3.

____

____

____

____

6. 4, 8, 32

____

____

____

____

Write the related facts for the set of numbers.

Complete the related facts.

2 × 6 = 126 × 2 = 1212 ÷ 2 = 612 ÷ 6 = 2

10. CDs are on sale for $5 each. Jennifer

has $45 and wants to buy as many

as she can. How many CDs can

Jennifer buy?

11. Mr. Moore has 21 feet of wallpaper.

He cuts it into sections that are each

3 feet long. How many sections does

Mr. Moore have?

7. 4 × 9 = _

9 × _ = 36

36 ÷ _ = 4

_÷ 4 = 9

8. _ × 7 = 35

_ × 5 = 35

_ ÷ 7 = 5

35 ÷ 5 = _

9. 6 × _ = 18

3 × 6 = _

18 ÷ _ = 3

_ ÷ 3 = 6

Lesson 6.8ALGEBRA

COMMON CORE STANDARD—3.OA.7 Multiply and divide within 100.

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Spiral Review (3.OA.1, 3.OA.5, 3.OA.7, 3.NBT.3)

3. Beth runs 20 miles each week for

8 weeks. How many miles does Beth

run in 8 weeks?

5. Uri’s bookcase has 5 shelves.

There are 9 books on each shelf. How

many books are in Uri’s bookcase?

4. Find the product.

5 × 0

6. There are 6 batteries in one

package. How many batteries

will 6 packages have?

1. What number completes the

set of related facts?

5 × = 40 40 ÷ = 5

× 5 = 40 40 ÷ 5 =

2. Write the related facts for the set of

numbers.

4, 7, 28



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Chapter 6 P111

Division Rules for 1 and 0Lesson 6.9

ALGEBRA

Find the quotient.

1. 3 ÷ 1 = _ 2. 8 ÷ 8 = _ 3. _ = 0 ÷ 6 4. 2 ÷ 2 = _

5. _= 9 ÷ 1 6. 0 ÷ 2 = _ 7. 0 ÷ 3 = _ 8. _= 0 ÷ 4

9. 7q w 7 10. 1q w 6 11. 9q w 0 12. 1q w 5

3

17. There are no horses in the stables.

There are 3 stables in all. How many

horses are in each stable?

18. Jon has 6 kites. He and his friends

will each fly 1 kite. How many

people in all will fly a kite?

13. 1q w 0 14. 4q w 4 15. 1q ww 10 16. 2q w 2

COMMON CORE STANDARD—3.OA.5Understand properties of multiplication and the relationship between multiplication and division.

0 3 6 9 12 15 18 21

Lee

Sam

Number of Cans

Stud

ents

Can Food Drive

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3. There are 7 plates on the table.

There are 0 sandwiches on each

plate. How many sandwiches are

on the plates?

7 × 0

5. Describe the pattern in the table.

Vans 1 2 3 4 5

Students 6 12 18 24 30

4. Show a way to break apart the array to

find the product.

6. Use the graph.

How many more cans did Sam bring

in than Lee?

1. Candace has 6 pairs of jeans.

She places each pair on its own

hanger. How many hangers does

Candace use?

2. There are 0 birds and 4 bird cages.

What division equation describes

how many birds are in each cage?


6 Letter dividend - 3rd Grade...

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